First I'd like to say
that I'm not a hundred percent sure of the following, But I am
I was trying to express the
inverse of a matrix for implementing it in my project.
way I worked is basically.
If P1 = [M] * P2
we can express P1, extract the original X,Y and Z, and then group
the transformed X,Y and Z and get the values of the inverse
Doing this I got an expression which is similar
to the matrix you got except with a pretty large denominator.
refering to the inverse matrix described on this
of course started thinking and it seems logical that there will be
a denominator, since you're trying to take apart and regroup
values which requires you'll find a common denominator.
I think the problam is you asumed that [b]*[b]^(-1)=[i].
I would think that:
Sx, 0, 0, 0
0, Sy, 0, 0
0, 0, Sz, 0
Where Sx, Sy and Sz are
the scaling about each axis.
This will of course produce
So the matrix you got would be the
specific case where the scale matrix is [I] which could be useful
in certain cases where you know that the scaling is 1 but is not
the general inverse of a matrix.
Can you verify